Name:_________________________________
Date:__________ Period:__________
Algebra 2 Ch.8 Test
Use a Table and Graph each function.
2. y 
1. y  3(2) x
x
-2
1
(4) x
2
x
-2
y
-1
-1
0
0
1
1
2
2
y
3. Write an exponential function of the form y  ab x that includes the given points (2, 122.5) and (3, 857.5).
4. Happy graduation!! You’ve collected a total of $4000 from all of the graduation cards and gifts from friends
and family...WOAH! Unfortunately, your dad tells you that you have to keep half of it in the bank. So you put
half into an account earning 4% interest compounded continuously. How much money will you have if you
keep it there for 8 years without touching it?
Describe how the graph of each function is related to the graph of its parent function.
5. y  3 x 4
6. y  5 x 1  2
Evaluate each logarithm using the change of base formula.
1
7. log 1
8. log 3 729
4
2
9. log 9
1
3
Name:_________________________________
Date:__________ Period:__________
Graph the logarithmic function and its inverse.
10. y  log 4 x
x
y
-2
-1
0
Inverse:_______________
1
Write each logarithmic expression as a single logarithm.
11. log 2  3 log 5
12. log a  log ab
Expand each logarithm.
13. log 5 6 x
x2 y
14. log 5 4
z
Write each expression as a single natural logarithm.
15. 2 ln 10  ln 5
16. 5 ln a  3 ln b
Use the properties of logarithms to evaluate each expression.
17. log 5  log 10  log 2
18. log 8 4  log 8 16
Solve each equation. Round to the nearest hundredth.
19. log 5 x  3
20. 10 2 x  40
21. log 5 (3x  10)  3 log 5 4  2
22. 8 x 1  12
Name:_________________________________
Date:__________ Period:__________
23. The adult population of Denver is 1,150,000. A consultant to a law firm uses the function
P  1150000(1  e 0.03t ) to estimate the number of people, P, who have heard about a major crime t days after
the crime was first reported. About how many days does it take for 60% of the population to have been exposed
to the news of the crime? (Hint: 60% = population x 0.6)
Use the properties of logarithms to simplify each equation and solve it. Round to the nearest hundredth.
24. ln( x  3)  1
25. 2 ln x  ln 3  2
26. e 3 x  12
27. A manufacturer bought a new rolling press for $48000. It has depreciated in value at an annual rate of 15%.
What is the value 5 years after he purchased it? Round to the nearest hundred dollars.
28. Hg-197 is used in Kidney scans. It has a half-life of 64 hr.
a) Write the exponential decay function for a 12-mg sample.
b) Find the amount remaining after 96 hr.
EXTRA CREDIT:
Show that solving the equation 3 2 x  4 by taking common logarithms (base 10) of both sides is equivalent to
solving it by taking logarithms to the base 3 of both sides.